Let \(M\) be a manifold with boundary . Then \(\Int M \subset M\) is open and a manifold with no boundary .
Proof
Let \(p\in \Int M\). Then there is an interior chart \((U,\varphi)\) with \(p\in U\). For every \(q\in U\) the chart \((U,\varphi)\) is also an interior chart. Therefore there is a open neighbourhood lying in \(\Int M\) and according to (0x677a9732)
\(\Int M\) is open.
Remarks
- Since \(\Int M\) is open, the boundary \(\partial M\) is closed .